Priyansh Bajaj AskiitiansExpert-IITD
Last Activity: 14 Years ago
Dear Vipul,
Solution:- Given, AC = a BC and BC = a AB. We want to find AC: AB = a2
Since, AC is the diameter of the circle, it subtends 900 angle at B. Let, AC = 'd' and angle C be 'x'. Then,
AB = d sinx , and BC = d cosx
So, AC = a BC will give 1 = a cosx or cosx = 1/a
And, BC = a AB will give cos x = a sinx
Since, cos x = 1/a, sin x = √(a2 -1) / a
So, 1 = a √(a2 -1) or a4 - a2 -1 = 0
On solving quad. eq., we'll get - a2 = (√5 +1) / 2 [ANS]
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All the best Vipul!!!
Regards,
Askiitians Experts
Priyansh Bajaj